Internet Security Cryptographic Principles, Algorithms and Protocols - Chapter 3 ppt

3 Symmetric Block Ciphers This chapter deals with some important block ciphers that have been developed in the past. They are IDEA (1992), RC5 (1995), RC6 (1996), DES (1977) and AES (2001). The Advanced Encryption Standard (AES) specifies a FIPS-approved symmetric block cipher which will soon come to be used in lieu of Triple DES or RC6. 3.1 Data Encryption Standard (DES) In the late 1960s, IBM initiated a Lucifer research project, led by Horst Feistel, for computer cryptography. This project ended in 1971 and LUCIFER was first known as a block cipher that operated on blocks of 64 bits, using a key size of 128 bits. Soon after this IBM embarked on another effort to develop a commercial encryption scheme, which was later called DES. This research effort was led by Walter Tuchman. The outcome of this effort was a refined version of Lucifer that was more resistant to cryptanalysis. In 1973, the National Bureau of Standards (NBS), now the National Institute of Standards and Technology (NIST), issued a public request for proposals for a national cipher standard. IBM submitted the research results of the DES project as a possible candidate. The NBS requested the National Security Agency (NSA) to evaluate the algo- rithm’s security and to determine its suitability as a federal standard. In November 1976, the Data Encryption Standard was adopted as a federal standard and authorised for use on all unclassified US government communications. The official description of the standard, FIPS PUB 46, Data Encryption Standard was published on 15 January 1977. The DES algorithm was the best one proposed and was adopted in 1977 as the Data Encryption Standard even though there was much criticism of its key length (which had changed from Lucifer’s original 128 bits to 64 bits) and the design criteria for the internal structure of DES, i.e., S-box. Nevertheless, DES has survived remarkably well over 20 years of intense cryptanalysis and has been a worldwide standard for over 18 years. The recent work on differential cryptanalysis seems to indicate that DES has a very strong internal structure. Internet Security. Edited by M.Y. Rhee  2003 John Wiley & Sons, Ltd ISBN 0-470-85285-2 58 INTERNET SECURITY Since the terms of the standard stipulate that it be reviewed every five years, on 6 March 1987 the NBS published in the Federal Register a request for comments on the second five-year review. The comment period closed on 10 December 1992. After much debate, DES was reaffirmed as a US government standard until 1992 because there was still no alternative for DES. The NIST again solicited a review to assess the continued adequacy of DES to protect computer data. In 1993, NIST formally solicited comments on the recertification of DES. After reviewing many comments and technical inputs, NIST recommend that the useful lifetime of DES would end in the late 1990s. In 2001, the Advanced Encryption Standard (AES), known as the Rijndael algorithm, became an FIPS- approved advanced symmetric cipher algorithm. AES will be a strong advanced algorithm in lieu of DES. The DES is now a basic security device employed by worldwide organisations. There- fore, it is likely that DES will continue to provide network communications, stored data, passwords and access control systems. 3.1.1 Description of the Algorithm DES is the most notable example of a conventional cryptosystem. Since it has been well documented for over 20 years, it will not be discussed in detail here. DES is a symmetric block cipher, operating on 64-bit blocks using a 56-bit key. DES encrypts data in blocks of 64 bits. The input to the algorithm is a 64-bit block of plaintext and the output from the algorithm is a 64-bit block of ciphertext after 16 rounds of identical operations. The key length is 56 bits by stripping off the 8 parity bits, ignoring every eighth bit from the given 64-bit key. As with any block encryption scheme, there are two inputs to the encryption function: the 64-bit plaintext to be encrypted and the 56-bit key. The basic building block of DES is a suitable combination of permutation and substitution on the plaintext block (16 times). Substitution is accomplished via table lookups in S-boxes. Both encryption and decryption use the same algorithm except for processing the key schedule in the reverse order. The plaintext block X is first transposed under the initial permutation IP, giving X 0 = IP(X) = (L 0 ,R 0 ). After passing through 16 rounds of permutation, XORs and sub- stitutions, it is transposed under the inverse permutation IP −1 to generate the ciphertext block Y. If X i = (L i ,R i ) denotes the result of the ith round encryption, then we have L i = R i−1 R i = L i−1 ⊕ f (R i−1 ,K i ) The ith round encryption of DES algorithm is shown in Figure 3.1. The block diagram for computing the f( R, K)-function is shown in Figure 3.2. The decryption process can be derived from the encryption terms as follows: R i−1 = L i L i−1 = R i ⊕ f (R i−1 ,K i ) = R i ⊕ f (L i ,K i ) If the output of the ith round encryption be L i ||R i , then the corresponding input to the (16– i)th round decryption is R i ||L i . The input to the first round decryption is equal to SYMMETRIC BLOCK CIPHERS 59 f(R i−1 , K i ) L i−1 R i−1 K i R i L i Figure 3.1 The ith round of DES algorithm. R i−1 (32 bits) E(R i−1 ) (48 bits) (48 bits) S 1 S 3 S 2 S 4 S 5 S 6 S 7 S 8 P(Ω i ) f(R i−1 , K i ) (32 bits) K i Σ = Ω i (32 bits) || 6 6 6 6 6 6 6 6 4 4 4 4 4 4 4 4 S-boxes Γ i = E(R i−1 ) + K i Figure 3.2 Computation of the f-function. 60 INTERNET SECURITY the 32-bit swap of the output of the 16th round encryption process. The output of the first round decryption is L 15 ||R 15 , which is the 32-bit swap of the input to the 16th round of encryption. 3.1.2 Key Schedule The 64-bit input key is initially reduced to a 56-bit key by ignoring every eighth bit. This is described in Table 3.1. These ignored 8 bits, k 8 ,k 16 ,k 24 ,k 32 ,k 40 ,k 48 ,k 56 ,k 64 are used as a parity check to ensure that each byte is of old parity and no errors have entered the key. After the 56-bit key was extracted, they are divided into two 28-bit halves and loaded into two working registers. The halves in registers are shifted left either one or two positions, depending on the round. The number of bits shifted is given in Table 3.2. After being shifted, the halves of 56 bits (C i ,D i ), 1 ≤ i ≤ 16, are used as the key input to the next iteration. These halves are concatenated in the ordered set and serve as input to the Permuted Choice 2 (see Table 3.3), which produces a 48-biy key output. Thus, a different 48-bit key is generated for each round of DES. These 48-bit keys, K 1 ,K 2 , , K 16 , are used for encryption at each round in the order from K 1 through K 16 . The key schedule for DES is illustrated in Figure 3.3. With a key length of 56 bits, these are 2 56 = 7.2 ×10 16 possible keys. Assuming that, on average, half the key space has to be searched, a single machine performing one DES encryption per µs would take more than 1000 years to break the cipher. Therefore, a brute-force attack on DES appears to be impractical. Table 3.1 Permuted choice 1 (PC-1) 57 49 41 33 25 17 9 1 58 50 42 34 26 18 10 2 59 51 43 35 27 19 11 3 60 52 44 36 63 55 47 39 31 23 15 7 62 54 46 38 30 22 14 661534537292113 5282012 4 Table 3.2 Schedule for key shifts Round number 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Number of left shifts 112222221 2 2 2 2 2 2 1 Table 3.3 Permuted choice 2 (PC-2) 14 17 11 24 1 5 3 28 15 6 21 10 23 19 12 4 26 8 16 7 27 20 13 2 41 52 31 37 47 55 30 40 51 45 33 48 44 49 39 56 34 53 46 42 50 36 29 32 TEAMFLY Team-Fly ® SYMMETRIC BLOCK CIPHERS 61 Key input (64 bits) PC-1 56 bits 28 bits 28 bits 28 bits 28 bits | | 28 bits 28 bits PC-2 K 1 | | 28 bits 28 bits PC-2 K 2 28 bits 28 bits | | PC-2 K 16 C 0 LS (1) C 1 LS (1) C 2 LS (2) C 3 C 16 D 0 LS (1) D 1 LS (1) D 2 LS (2) D 3 D 16 48 bits 48 bits 48 bits Figure 3.3 Key schedule for DES. 62 INTERNET SECURITY Example 3.1 Assume that a 64-bit key input is K = 581fbc94d3a452ea, including 8 parity bits. Find the first three round keys only: K 1 ,K 2 ,andK 3 . The register contents C 0 (left) and D 0 (right) are computed using Table 3.1: C 0 = bcd1a45 D 0 = d22e87f Using Table 3.2, the blocks C 1 and D 1 are obtained from the block C 0 and D 0 by shifting one bit to the left as follows: C 1 = 79a348b D 1 = a45d0ff The 48-bit key K 1 is derived using Table 3.3 (PC-2) by inputting the concatenated block (C 1 ||D 1 ) such that K 1 = 27a169e58dda. The concatenated block (C 2 ||D 2 ) is computed from (C 1 ||D 1 ) by shifting one bit to the left as shown below: (C 2 ||D 2 ) = f346916 48ba1ff Using Table 3.3 (PC-2), the 48-bit key K 2 at round 2 is computed as K 2 = da91ddd7b748. Similarly, (C 3 ||D 3 ) is generated from shifting (C 2 ||D 2 ) by two bits to the left as follows: (C 3 ||D 3 ) = cd1a456 22e87fd Using Table 3.3, we have K 3 = 1dc24bf89768 In a similar fashion, all the other 16-round keys can be computed and the set of entire DES keys is listed as follows: K 1 = 27a169e58dda K 2 = da91ddd7b748 K 3 = 1dc24bf89768 K 4 = 2359ae58fe2e K 5 = b829c57c7cb8 K 6 = 116e39a9787b K 7 = c535b4a7fa32 K 8 = d68ec5b50f76 K 9 = e80d33d75314 K 10 = e5aa2dd123ec K 11 = 83b69cf0ba8dK 12 = 7c1ef27236bf K 13 = f6f0483f39ab K 14 = 0ac756267973 K 15 = 6c591f67a976 K 16 = 4f57a0c6c35b 3.1.3 DES Encryption DES operates on a 64-bit block of plaintext. After initial permutation, the block is split into two blocks L i (left) and R i (right), each 32 bits in length. This permuted plaintext SYMMETRIC BLOCK CIPHERS 63 Table 3.4 Initial permutation (IP) 58 50 42 34 26 18 10 2 L i 60 52 44 36 28 20 12 4 62 54 46 38 30 22 14 6 64 56 48 40 32 24 16 8 57 49 41 33 25 17 9 1 R i 59 51 43 35 27 19 11 3 61 53 45 37 29 21 13 5 63 55 47 39 31 23 15 7 Table 3.5 E bit-selection table 32 12345 4 56789 8 910111213 12 13 14 15 16 17 16 17 18 19 20 21 20 21 22 23 24 25 24 25 26 27 28 29 28 29 30 31 32 1 (see Table 3.4) has bit 58 of the input as its first bit, bit 50 as its second bit, and so on down to bit 7 as the last bit. The right half of the data, R i , is expanded to 48 bits according to Table 3.5 of an expansion permutation. The expansion symbol E of E( R i ) denotes a function which takes the 32-bit R i as input and produces the 48-bit E( R i ) as output. The purpose of this operation is twofold – to make the output the same size as the key for the XOR operation, and to provide a longer result that is compressed during the S-box substitution operation. After the compressed key K i is XORed with the expanded block E(R i−1 ) such that  i = E(R i−1 ) ⊕ K i for 1 ≤ i ≤ 15, this 48-bit  i moves to substitution operations that are performed by eight S i -boxes. The 48-bit  i is divided into eight 6-bit blocks. Each 6-bit block is operated on by a separate S i -box, as shown in Figure 3.2. Each S i -box is a table of 4 rows and 16 columns as shown in Table 3.6. This 48-bit input  i to the S-boxes are passed through a nonlinear S-box transformation to produce the 32- bit output. If each S i denotes a matrix box defined in Table 3.6 and A denotes an input block of 6 bits, then S i (A) is defined as follows: the first and last bits of A represent the row number of the matrix S i , while the middle 4 bits of A represent a column number of S i in the range from 0 to 15. For example, for the input (101110) to S 5 -box, denote as S 10 5 (0111), the first and last bits combine to form 10, which corresponds to the row 2 (actually third row) of S 5 .The 64 INTERNET SECURITY Table 3.6 S-boxes 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0 14 413 1 21511 8 310 612 5 9 0 7 S 1 1 0157414213110612119538 2 4114813621115129731050 3 1512824917511314100613 0 15 1 8 14 6 11 3 4 9 7 2 13 12 0 5 10 S 2 1 313 4 715 2 81412 0 110 6 911 5 2 0147111041315812693215 3 13 810 1 315 4 211 6 712 0 514 9 0 1009146315511312711428 S 3 1 1370934610285141211151 2 1364981530111212510147 3 1101306987415143115212 0 7131430691012851112415 S 4 1 13 811 5 615 0 3 4 7 212 11014 9 2 1069012117131513145284 3 3150610113894511127214 0 2124171011685315130149 S 5 1 1411212471315015103986 2 4211110137815912563014 3 1181271142136150910453 0 1211015926801334147511 S 6 1 1015427129561131401138 2 9141552812370410113116 3 4321295151011141760813 0 4112141508133129751061 S 7 1 13 011 7 4 9 11014 3 512 215 8 6 2 1 4 11 13 12 3 7 14 10 15 6 8 0 5 9 2 3 6111381410795015142312 0 13 2 8 4 61511 110 9 314 5 012 7 S 8 1 1151381037412561101492 2 7114191214206101315358 3 2114741081315129035611 middle 4 bits combine to form 0111, which corresponds to the column 7 (actually the eighth column) of the same S 5 -box. Thus, the entry under row 2, column 7 of S 5 -box is computed as: S 10 5 (0111) = S 2 5 (7) = 8 (hexadecimal) = 1000 (binary) Thus, the value of 1000 is substituted for 101110. That is, the four-bit output 1000 from S 5 is substituted for the six-bit input 101110 to S 5 . Eight four-bit blocks are the S-box output resulting from the substitution phase, which recombine into a single 32-bit block  i by concatenation. This 32-bit output  i of the S-box substitution are permuted according to Table 3.7. This permutation maps each input bit of  i to an output position of P( i ). SYMMETRIC BLOCK CIPHERS 65 Table 3.7 Permutation function P 16 7 20 21 29 12 28 17 1152326 5183110 2 8 24 14 32 27 3 9 19 13 30 6 22 11 4 25 Table 3.8 Inverse of initial permutation, IP −1 408481656246432 397471555236331 386461454226230 375451353216129 364441252206028 353431151195927 342421050185826 33 1 41 9 49 17 57 25 The output P( i ) are obtained from the input  i by taking the 16th bit of  i as the first bit of P(  i ), the seventh bit as the second bit of P( i ), and so on until the 25th bit of  i is taken as the 32nd bit of P( i ). Finally, the permuted result is XORed with the left half L i of the initial permuted 64-bit block. Then the left and right halves are swapped and another round begins. The final permutation is the inverse of the initial permutation, and is described in Table 3.8 IP −1 . Note here that the left and right halves are not swapped after the last round of DES. Instead, the concatenated block R 16 ||L 16 is used as the input to the final permutation of Table 3.8 (IP −1 ). Thus, the overall structure for DES algorithm is shown in Figure 3.4. Example 3.2 Suppose the 64-bit plaintext is X = 3570e2f1ba4682c7, and the same key as used in Example 3.1, K = 581fbc94d3a452ea is assumed again. The first two-round keys are, respectively, K 1 = 27a169e58dda and K 2 = da91ddd76748. For the purpose of demonstration, the DES encryption aims to limit the first two rounds only. The plaintext X splits into two blocks (L 0 ,R 0 ) using Table 3.4 IP such that L 0 = ae1ba189 and R 0 = dc1f10f4. The 32-bit R 0 is expanded to the 48-biy E(R 0 ) such that E(R 0 ) = 6f80fe8a17a9. The key-dependent function  i is computed by XORing E(R 0 ) with the first round key K 1 , such that  1 = E(R 0 ) ⊕ K 1 = 4821976f9a73 66 INTERNET SECURITY X 64 bits 32 bits 32 bits 48 bits K 1 32 bits 32 bits 48 bits 48 bits K 2 Plaintext input IP K 64 bits 28 bits Key input PC-1 56 bits 28 bits K 16 Y 64 bits PC-2 PC-2 D 0 LS D 1 LS D 2 LS D 3 C 0 LS C 1 LS C 2 LS C 3 PC-2 R 1 = P(Ω 1 ) ⊕ L 0 R 2 = P(Ω 2 ) ⊕ L 1 32 bits Ω 1 (32 bits) S 1 S 8 Γ 1 = E(R 0 ) ⊕ K 1 (48 bits) Γ 2 = E(R 1 ) ⊕ K 2 (48 bits) Ω 2 (32 bits) S 1 S 8 Γ 16 = E(R 15 ) ⊕ K 16 (48 bits) Ω 16 (32 bits) S 1 S 8 R 0 E(R 0 ) E(R 1 ) P(Ω 2 ) P(Ω 1 ) E(R 15 ) P(Ω 16 ) L 16 = R 15 32 bits R 16 = P(Ω 16 ) ⊕ L 15 L 0 L 1 = R 0 32 bits L 2 = R 1 L 15 R 15 IP −1 Ciphertext output Figure 3.4 Block cipher design of DES. [...]... = 34 687255, B = L[2] = 35 340975 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 TE Round Value Round 90 INTERNET SECURITY Team-Fly® SYMMETRIC BLOCK CIPHERS 91 3. 3 .3 Encryption The input block to RC5 consists of two w-bit words given in two registers, A and B The output is also placed in the registers A and B Recall that RC5 uses an expanded... = f3f0 −Z44 = 70c4 Z−1 = 33 05 46 Z41 = 6b42 Z42 = 9f67 Z−1 = c579 37 −Z39 = f7ec −Z38 = 61fa Z−1 = bf28 40 Z35 = a14f Z36 = b3e0 Z−1 = c53c 31 −Z 33 = e841 −Z32 = fcfc Z−1 = 37 03 34 Z29 = a7d9 Z30 = f010 Z−1 = cc14 25 −Z27 = 2008 −Z26 = ff75 Z−1 = 24f6 28 Z 23 = ecf8 Z24 = 0871 Z−1 = 439 6 19 −Z21 = 03f3 −Z20 = ba11 Z−1 = dfa7 22 Z17 = e781 Z18 = 8205 Z−1 = 18a7 13 −Z15 = f94c −Z14 = 0802 Z−1 = 9a 13 16... 0x260b152f31b51c68 K2 = 0x321f0d61a773b558 K3 = 0x519b 733 1bf104ce3 and the plaintext P = 0x403da8a295d3fed9 The 16-round keys corresponding to each given key K1, K2 and K3 are computed as shown below Round K1 K2 K3 1 2 3 4 5 6 7 000ced9158c9 588490792e94 54882eb9409b a2a006077207 280e26b621e4 e 030 38a08bc7 84867056a6 93 5a1ec4b60e98 710c31 833 4c6 c5a8b4ec83a5 96a696124ecf 7e16225e9191 ea906c 836 569 88c25e6abb00... Table 3. 12 IDEA encryption and decryption subkeys Round Encryption subkeys Decryption subkeys 1 2 3 4 5 6 7 8 9 Z1 Z2 Z3 Z4 Z5 Z6 Z7 Z8 Z9 Z10 Z11 Z12 Z 13 Z14 Z15 Z16 Z17 Z18 Z19 Z20 Z21 Z22 Z 23 Z24 Z25 Z26 Z27 Z28 Z29 Z30 Z31 Z32 Z 33 Z34 Z35 Z36 Z37 Z38 Z39 Z40 Z41 Z42 Z 43 Z44 Z45 Z46 Z47 Z48 Z49 Z50 Z51 Z52 Z−1 − Z50 − Z51 Z−1 Z47 Z48 49 52 Z−1 − Z45 − Z44 Z−1 Z41 Z42 43 46 Z−1 − Z39 − Z38 Z−1 Z35 Z36... CIPHERS Table 3. 10 Z1 = 5a14 Z2 = fb3e Z3 = 021c Z4 = 79e0 Z5 = 6081 Z6 = 46a0 Z7 = 117b Z8 = ff 03 Z9 = 7c04 Z10 = 38 f3 Z11 = c0c1 Z12 = 028d Z 13 = 4022 Z14 = f7fe Z15 = 06b4 Z16 = 29f6 Z17 = e781 Z18 = 8205 Z19 = 1a80 Z20 = 45ef Z21 = fc0d Z22 = 68 53 Z 23 = ecf8 Z24 = 0871 Z25 = 0a35 Z26 = 008b 79 Subkeys for encryption Z27 Z28 Z29 Z30 Z31 Z32 Z 33 Z34 Z35 Z36 Z37 Z38 Z39 Z40 Z41 Z42 Z 43 Z44 Z45 Z46... K11 = 851b 633 6a3a3 K 13 = 1d57c04ea3da K15 = 9dc1456a946a K2 = 6e26890ddd29 K4 = 48a8dae9cb3c K6 = e22d02dd1 235 K8 = c5b41a30bb95 K10 = b0d 331 a373c7 K12 = a372d5f60d47 K14 = 5251f975f549 K16 = 9f2d1a5ad5fa The 64-bit plaintext X splits into two blocks (L0 , R0 ), according to Table 3. 4 (IP), such that L0 = 4713b8f4 R0 = 5cd9b326 The 32 -bit R0 is spread out and scrambled in 48 bits, using Table 3. 5, such... 30 258f25c11d 93e853d116b1 cc4a1fa9f254 27b30c31c6a6 0a1ce39c0c87 f968788e62d5 84e78 833 e3c1 521f17b285 03 6db841ce2706 c 931 3c0591e3 Encryption: Compute the ciphertext C through the EDE mode operation of P Each stage in the triple DES-EDE sequence is computed as: First stage: EK1 = 0x7a39786f7ba3 234 9 Second stage: DK2 = 0x9c60f8 536 9113aea Third stage: EK3 = 0xe22ae 334 94beb 930 = C (ciphertext) Decryption: Using... 91) Z26 = Z(92, 93, , 107) Z27 = Z(108, 109, , 1 23) Z28 = Z(124, 125, , 128, 1, 2, , 11) Z29 = Z(12, 13, , 27) Z30 = Z(28, 29, , 43) Round 6 Z31 = Z(44, 45, , 59) Z32 = Z(60, 61, , 75) Z 33 = Z(101, 102, , 115) Z34 = Z(117, 118, , 128, 1, 2, 3, 4) Z35 = Z(5, 6, , 20) Z36 = Z(21, 22, , 36 ) Round 7 Z37 = Z (37 , 38 , , 52) Z38 = Z( 53, 54, , 68) Z39 = Z(69, 70, ... 88c25e6abb00 03e4ee7c63c8 8486dd46ac65 575a226a8ddc aab9e009d59b 98664f4f5421 615718ca496c 4499e580db9c SYMMETRIC BLOCK CIPHERS 73 Round K1 K2 K3 8 9 10 11 12 13 14 15 16 c65a127f0549 24 432 36696a6 a311155c0deb 0d02d10ed859 1750b843f570 9e01c0a98d28 1a4a0dc85e16 0 931 0c5d42bc 532 48c80ee34 245b3af0453e 76d38087dd44 1a915708a7f0 2d405ff9cc05 2741ac4a469a 9a09b19d710d 9d2a39a252e0 8 736 8cd0ab27 30 258f25c11d 93e853d116b1... 0 1 2 3 4 5 6 7 8 9 10 11 12 5c5f001d aacdcf78 b2c9dafc 36 2f2508 ace3d 838 6ad30720 3cc6723c c217 734 4 436 ee2fe fac6db42 6a18 039 7 e07e082e ac13c0f7 eaa518ac 073A31fa d0506098 67cccf55 5f84483d d77180e6 accd0d34 9954851d f7702871 91c5af 63 f 631 31f5 816fc2b3 52892b5b Ciphertext = ac13c0f7 52892b5b 92 INTERNET SECURITY 3. 3.4 Decryption RC5 decryption is given in the pseudocode as shown below For i = r down . 6 64 56 48 40 32 24 16 8 57 49 41 33 25 17 9 1 R i 59 51 43 35 27 19 11 3 61 53 45 37 29 21 13 5 63 55 47 39 31 23 15 7 Table 3. 5 E bit-selection table 32 1 234 5 4 56789 8 9101112 13 12 13 14 15 16. 014711104 131 58126 932 15 3 13 810 1 31 5 4 211 6 712 0 514 9 0 100914 631 551 131 2711428 S 3 1 137 0 934 610285141211151 2 136 4981 530 111212510147 3 110 130 69874151 431 15212 0 7 131 430 691012851112415 S 4 1 13 811. 0 3 4 7 212 11014 9 2 1069012117 131 5 131 45284 3 31506101 138 94511127214 0 212417101168 531 5 130 149 S 5 1 141121247 131 50151 039 86 2 4211110 137 8159125 630 14 3 1181271142 136 1509104 53 0 121101592680 133 4147511 S 6 1